The 24-year-old midfielder had been expected to leave Goodison Park over the summer but a move to Chelsea fell through at the final stages.
There is interest in Barkley from Arsenal, Manchester City and Tottenham Hotspur, with Spurs reportedly leading the way to securing the midfielder’s signature before the end of the January transfer window.
Speaking in his weekly press conference, Allardyce said: ”I think that we are resigned and the club was resigned before I got here that we're going to lose Ross and I can't see that changing.
"I expect there would be some interest some time in this window if there's going to be any interest from one of the ‘big boys’.”
Barkley is out of contract in the summer and is able to discuss a free transfer with clubs during this window. However, the midfielder could return for the Blues’ first-team before he moves away from Goodison Park.
"He's back in training full-time," added Allardyce. "It's a little bit like James McCarthy and Yannick Bolasie. When he comes back the touch won't be quite as good as it used to be and the match fitness won't be quite as good as it used to be.”
Time to say goodbye
There had been hope from some at the club that the midfielder could have signed a new contract with his boyhood club when Ronald Koeman left.
Rumours had surfaced towards the end of last season that Barkley had fallen out with the former Everton boss and that was the root of his wish to leave the club.
Koeman stated at the end of the last campaign that he expected the midfielder to leave over the summer and signed Davy Klaassen, Wayne Rooney and Gylfi Sigurdsson as players who could replace Barkley in his team.
Only Rooney, a boyhood blue who left the club himself at an early age, has been able to replace the quality lost in the line-up with Barkley sidelined.